Analyses for ‘A Translational Paradigm to Study the Effects of Uncontrollable Stress in Humans’
Study 2 Analysis
Laura E. Meine and Katja Schueler
25.06.2020
1 Summary
This script runs analyses on data from study 2. Specifically, it compares data from two groups of participants who underwent escapable stress (EC) or yoked inescapable stress (YC), respectively. We use the terms “group” and “condition” interchangeably. . Measurements under investigation comprised reaction times (RTs) and ratings under acute stress (stressor aversiveness, control, exhaustion, helplessness) as well as pre-post changes in affective state (STADI and PANAS questionnaires), and effects escape behaviour (activity, exploration, escapes, efficiency).
2 Sample Descriptives
In total, the sample consisted of N = 100 participants with n = 62 in EC and n = 38 in YC.
2.1 Age & Sex
3 A priori Group Difference Checks
3.1 Sex (Chi-square Test)
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: demo$condition and demo$sex
## X-squared = 0.061738, df = 1, p-value = 0.8038There were no a priori group differences in male-female ratio.
3.2 Age (t-test)
##
## Two Sample t-test
##
## data: demo$age[demo$condition == "EC"] and demo$age[demo$condition == "YC"]
## t = -1.758, df = 98, p-value = 0.08186
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3.169705 0.191776
## sample estimates:
## mean of x mean of y
## 22.77419 24.26316##
## Cohen's d
##
## d estimate: -0.362193 (small)
## 95 percent confidence interval:
## lower upper
## -0.77418265 0.04979672There were some outliers and we checked for the 2 extreme cases but rerunning all analyses without those did not change the results, so we kept them. Overall, there were no differences in age across groups.
3.3 Level of Education
## # A tibble: 1 x 8
## .y. group1 group2 n1 n2 statistic p p.signif
## <chr> <chr> <chr> <int> <int> <dbl> <dbl> <chr>
## 1 education_level EC YC 62 38 1102. 0.507 ns## # A tibble: 1 x 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 education_level EC YC 0.0669 62 38 smallThere were no a priori group differences with respect to level of education.
4 Manipulation Check
4.1 Verify Yoking of Stress Durations
##
## Two Sample t-test
##
## data: stress$stress_duration[stress$condition == "EC"] and stress$stress_duration[stress$condition == "YC"]
## t = -0.18889, df = 5998, p-value = 0.8502
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.10778855 0.08884256
## sample estimates:
## mean of x mean of y
## 7.855990 7.865463There were no overall differences in overall stress durations between EC and YC because YC participants were pseudoyoked to EC. Very slight timing inaccurracies are due to program execution differences. Note that durations across trials differ between groups. We deliberately introduced a discount of max. stress exposure in EC to enhance the feeling of control. In YC, we randomly shuffled stress durations obtained from EC to enhance the feeling of arbitrary stress durations outside the participant’s control.
4.2 Assess Performance in EC
8 EC participants had less than 30% correct trials, however, excluding them did not affect subsequent results, so we kept them.
4.3 Stressor Aversiveness
There were outliers with particularly low aversiveness ratings which we excluded from this analysis.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 10059.9 1 788.10 92 1174.3548 < 2e-16 ***
## condition 9.0 1 788.10 92 1.0555 0.30693
## sex 47.3 1 788.10 92 5.5259 0.02087 *
## trial 1.9 3 107.59 276 1.6168 0.18571
## condition:trial 0.4 3 107.59 276 0.3154 0.81422
## sex:trial 0.9 3 107.59 276 0.7977 0.49603
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.62968 6.0129e-08
## condition:trial 0.62968 6.0129e-08
## sex:trial 0.62968 6.0129e-08
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.75366 0.1976
## condition:trial 0.75366 0.7562
## sex:trial 0.75366 0.4653
##
## HF eps Pr(>F[HF])
## trial 0.7736208 0.1966629
## condition:trial 0.7736208 0.7617353
## sex:trial 0.7736208 0.4681660## Anova Table (Type 3 tests)
##
## Response: aversive_rating
## Effect df MSE F pes p.value
## 1 condition 1, 92 8.57 1.06 .01 .31
## 2 sex 1, 92 8.57 5.53 * .06 .02
## 3 trial 2.26, 208.01 0.52 1.62 .02 .20
## 4 condition:trial 2.26, 208.01 0.52 0.32 .003 .76
## 5 sex:trial 2.26, 208.01 0.52 0.80 .009 .47
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Both EC and YC rated the stressor as very aversive (global M = 5.3585859). Mean aversiveness ratings did not differ between groups. Stressor aversiveness ratings remained constant over time. Men reported lower stressor aversiveness compared to women.
4.4 Perceived Stressor Controllability
There were some outliers with respect to perceived control and we excluded them since this changed results significantly.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 2360.74 1 909.35 92 238.8376 < 2.2e-16 ***
## condition 198.43 1 909.35 92 20.0754 2.138e-05 ***
## sex 17.82 1 909.35 92 1.8027 0.182694
## trial 22.87 3 394.70 276 5.3309 0.001386 **
## condition:trial 10.01 3 394.70 276 2.3320 0.074445 .
## sex:trial 2.72 3 394.70 276 0.6338 0.593787
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.77114 0.00026196
## condition:trial 0.77114 0.00026196
## sex:trial 0.77114 0.00026196
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.84333 0.002667 **
## condition:trial 0.84333 0.085560 .
## sex:trial 0.84333 0.567551
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## HF eps Pr(>F[HF])
## trial 0.869147 0.002393656
## condition:trial 0.869147 0.083622038
## sex:trial 0.869147 0.572176992## Anova Table (Type 3 tests)
##
## Response: control_rating
## Effect df MSE F pes p.value
## 1 condition 1, 92 9.88 20.08 *** .18 <.0001
## 2 sex 1, 92 9.88 1.80 .02 .18
## 3 trial 2.53, 232.76 1.70 5.33 ** .05 .003
## 4 condition:trial 2.53, 232.76 1.70 2.33 + .02 .09
## 5 sex:trial 2.53, 232.76 1.70 0.63 .007 .57
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG## contrast estimate SE df t.ratio p.value
## X15 - X30 -0.4496 0.184 276 -2.446 0.0753
## X15 - X45 -0.4031 0.184 276 -2.193 0.1166
## X15 - X60 -0.7283 0.184 276 -3.962 0.0006
## X30 - X45 0.0465 0.184 276 0.253 0.8004
## X30 - X60 -0.2787 0.184 276 -1.516 0.2612
## X45 - X60 -0.3252 0.184 276 -1.769 0.2338
##
## Results are averaged over the levels of: condition, sex
## P value adjustment: holm method for 6 tests## Call:
## bwtrim(formula = control_rating ~ condition * factor(trial),
## id = ID, data = ratings_ctrl)
##
## value df1 df2 p.value
## condition 16.7247 1 54.3685 0.0001
## factor(trial) 3.5822 3 45.3750 0.0208
## condition:factor(trial) 3.3395 3 45.3750 0.0274We observed group differences in perceived control in the expected direction: YC reported lower control than EC. Overall perceived control increased over time (not clear why this would be the case in YC). After removal of outliers, there is a trend for an interaction of condition and trial which reflects EC’s learning curve with greater success in terminating the stressor over time.
5 RTs and Ratings During Stress Exposure
5.1 RTs
There were 3 outliers excluding them did not affect the results, so we kept them.
## Call:
## bwtrim(formula = rt ~ condition * trial, id = ID, data = stress)
##
## value df1 df2 p.value
## trial 1.0098 59 397.3603 0.4609
## condition 530.3995 1 970.8709 0.0000
## trial:condition 0.9437 59 397.7186 0.5958## [1] -0.8483162## [1] -0.2205065EC were significantly faster than YC. There was no effect of trial.
5.2 Exhaustion
There were no outliers with respect to exhaustion ratings.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 8080.9 1 1172.49 97 668.5348 < 2.2e-16 ***
## condition 29.6 1 1172.49 97 2.4524 0.120600
## sex 89.6 1 1172.49 97 7.4124 0.007681 **
## trial 16.8 3 241.78 291 6.7445 0.000206 ***
## condition:trial 1.7 3 241.78 291 0.7011 0.552033
## sex:trial 3.8 3 241.78 291 1.5198 0.209463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.61822 8.9693e-09
## condition:trial 0.61822 8.9693e-09
## sex:trial 0.61822 8.9693e-09
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.76833 0.0008058 ***
## condition:trial 0.76833 0.5163622
## sex:trial 0.76833 0.2182247
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## HF eps Pr(>F[HF])
## trial 0.7881077 0.0007168391
## condition:trial 0.7881077 0.5197865333
## sex:trial 0.7881077 0.2175475777## Anova Table (Type 3 tests)
##
## Response: exhausted_rating
## Effect df MSE F pes p.value
## 1 condition 1, 97 12.09 2.45 .02 .12
## 2 sex 1, 97 12.09 7.41 ** .07 .008
## 3 trial 2.30, 223.58 1.08 6.74 *** .07 .0008
## 4 condition:trial 2.30, 223.58 1.08 0.70 .007 .52
## 5 sex:trial 2.30, 223.58 1.08 1.52 .02 .22
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG## contrast estimate SE df t.ratio p.value
## X15 - X30 -0.406 0.134 291 -3.036 0.0131
## X15 - X45 -0.560 0.134 291 -4.192 0.0002
## X15 - X60 -0.189 0.134 291 -1.416 0.3185
## X30 - X45 -0.154 0.134 291 -1.156 0.3185
## X30 - X60 0.216 0.134 291 1.621 0.3185
## X45 - X60 0.371 0.134 291 2.776 0.0234
##
## Results are averaged over the levels of: condition, sex
## P value adjustment: holm method for 6 tests## Call:
## bwtrim(formula = exhausted_rating ~ condition * factor(trial),
## id = ID, data = ratings)
##
## value df1 df2 p.value
## condition 1.9905 1 73.6712 0.1625
## factor(trial) 6.9634 3 59.6649 0.0004
## condition:factor(trial) 0.9593 3 59.6649 0.4180
There were no group differences in terms of exhaustion ratings. Overall reported exhaustion increased, then decreased over time.
5.3 Feelings of Helplessness
There were no outliers with respect to helplessness ratings.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 7816.7 1 1165.51 97 650.5440 < 2.2e-16 ***
## condition 112.6 1 1165.51 97 9.3723 0.00285 **
## sex 21.5 1 1165.51 97 1.7933 0.18365
## trial 50.3 3 531.57 291 9.1875 7.944e-06 ***
## condition:trial 2.7 3 531.57 291 0.4880 0.69085
## sex:trial 1.3 3 531.57 291 0.2441 0.86550
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.78252 0.00027414
## condition:trial 0.78252 0.00027414
## sex:trial 0.78252 0.00027414
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.87585 2.387e-05 ***
## condition:trial 0.87585 0.6659
## sex:trial 0.87585 0.8404
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## HF eps Pr(>F[HF])
## trial 0.9024575 1.884721e-05
## condition:trial 0.9024575 6.715529e-01
## sex:trial 0.9024575 8.462020e-01## Anova Table (Type 3 tests)
##
## Response: helpless_rating
## Effect df MSE F pes p.value
## 1 condition 1, 97 12.02 9.37 ** .09 .003
## 2 sex 1, 97 12.02 1.79 .02 .18
## 3 trial 2.63, 254.87 2.09 9.19 *** .09 <.0001
## 4 condition:trial 2.63, 254.87 2.09 0.49 .005 .67
## 5 sex:trial 2.63, 254.87 2.09 0.24 .003 .84
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG## contrast estimate SE df t.ratio p.value
## X15 - X30 0.757 0.198 291 3.824 0.0008
## X15 - X45 0.644 0.198 291 3.251 0.0051
## X15 - X60 0.992 0.198 291 5.010 <.0001
## X30 - X45 -0.113 0.198 291 -0.573 0.5672
## X30 - X60 0.235 0.198 291 1.186 0.4733
## X45 - X60 0.348 0.198 291 1.759 0.2391
##
## Results are averaged over the levels of: condition, sex
## P value adjustment: holm method for 6 tests## Call:
## bwtrim(formula = helpless_rating ~ condition * factor(trial),
## id = ID, data = ratings)
##
## value df1 df2 p.value
## condition 12.5040 1 68.7409 0.0007
## factor(trial) 5.4474 3 60.8077 0.0022
## condition:factor(trial) 1.2419 3 60.8077 0.3024As expected, YC reported greater feelings of helplessness compared to EC. Overall helplessness ratings decreased across trials.
6 Changes in Affective State
6.1 Depression and Anxiety (STADI)
There were some outliers with respect to STADI scores but they did not represent extreme outliers, thus we kept them.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 235896 1 11570.7 97 1977.5808 < 2.2e-16 ***
## condition 443 1 11570.7 97 3.7106 0.056996 .
## sex 66 1 11570.7 97 0.5491 0.460471
## time 154 1 1355.6 97 11.0002 0.001283 **
## condition:time 3 1 1355.6 97 0.1955 0.659392
## sex:time 6 1 1355.6 97 0.4408 0.508312
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Anova Table (Type 3 tests)
##
## Response: STADI_S_Global
## Effect df MSE F pes p.value
## 1 condition 1, 97 119.29 3.71 + .04 .06
## 2 sex 1, 97 119.29 0.55 .006 .46
## 3 time 1, 97 13.97 11.00 ** .10 .001
## 4 condition:time 1, 97 13.97 0.20 .002 .66
## 5 sex:time 1, 97 13.97 0.44 .005 .51
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1## Call:
## bwtrim(formula = STADI_S_Global ~ condition * factor(time), id = ID,
## data = affStates)
##
## value df1 df2 p.value
## condition 2.9723 1 60.9630 0.0898
## factor(time) 9.4166 1 69.5219 0.0031
## condition:factor(time) 0.1273 1 69.5219 0.7223There was a trend effect of group with YC showing slightly higher scores than EC at pre and post. Although both groups reported an sig. increase in depressive symptoms and anxiety from pre to post stress induction, there was no interaction effect, i.e. no differential changes in STADI scores.
6.2 Positive and Negative Mood (PANAS)
6.2.1 Positive Mood
There were no outliers with respect to positive mood scores.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 142384 1 10798.7 97 1278.9635 < 2.2e-16 ***
## condition 21 1 10798.7 97 0.1857 0.66749
## sex 165 1 10798.7 97 1.4796 0.22679
## time 460 1 1976.7 97 22.5583 7.05e-06 ***
## condition:time 8 1 1976.7 97 0.3892 0.53420
## sex:time 137 1 1976.7 97 6.7410 0.01089 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Anova Table (Type 3 tests)
##
## Response: PANAS_pos
## Effect df MSE F pes p.value
## 1 condition 1, 97 111.33 0.19 .002 .67
## 2 sex 1, 97 111.33 1.48 .02 .23
## 3 time 1, 97 20.38 22.56 *** .19 <.0001
## 4 condition:time 1, 97 20.38 0.39 .004 .53
## 5 sex:time 1, 97 20.38 6.74 * .06 .01
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
There were no group differences in positive mood but an overall decrease from pre to post stress induction. Men displayed a slightly smaller decrease compared to women.
6.2.2 Negative Mood
There were some outliers with respect to negative mood but since they did not affect results, we kept them.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 36148 1 3338.9 97 1050.1721 < 2.2e-16 ***
## condition 268 1 3338.9 97 7.7901 0.006327 **
## sex 0 1 3338.9 97 0.0078 0.929725
## time 35 1 408.8 97 8.2540 0.004995 **
## condition:time 0 1 408.8 97 0.0646 0.799909
## sex:time 2 1 408.8 97 0.3594 0.550244
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Anova Table (Type 3 tests)
##
## Response: PANAS_neg
## Effect df MSE F pes p.value
## 1 condition 1, 97 34.42 7.79 ** .07 .006
## 2 sex 1, 97 34.42 0.01 <.0001 .93
## 3 time 1, 97 4.21 8.25 ** .08 .005
## 4 condition:time 1, 97 4.21 0.06 .0007 .80
## 5 sex:time 1, 97 4.21 0.36 .004 .55
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1## Call:
## bwtrim(formula = PANAS_neg ~ condition * factor(time), id = ID,
## data = affStates)
##
## value df1 df2 p.value
## condition 6.7716 1 57.8746 0.0117
## factor(time) 6.9370 1 69.6631 0.0104
## condition:factor(time) 0.0000 1 69.6631 0.9950There were sig. group differences in negative mood with slightly higher overall scores in YC compared to EC. We observed an overall decrease from pre to post stress induction but no interaction of group x time.
7 Escape Behaviour
7.1 Activity (moves per minute)
There were some outliers with respect to activity but few of them represented extreme deviations and it didn’t seem warranted to exclude them.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 51336095 1 8033840 97 619.8283 < 2.2e-16
## condition 78797 1 8033840 97 0.9514 0.331791
## sex 940303 1 8033840 97 11.3531 0.001082
## phase 3102641 1 3410501 97 88.2440 2.733e-15
## condition:phase 38452 1 3410501 97 1.0936 0.298269
## sex:phase 78431 1 3410501 97 2.2307 0.138539
## block 1024142 1 1896256 97 52.3884 1.075e-10
## condition:block 48237 1 1896256 97 2.4675 0.119481
## sex:block 28828 1 1896256 97 1.4747 0.227558
## trial 627173 4 2008659 388 30.2868 < 2.2e-16
## condition:trial 11529 4 2008659 388 0.5567 0.694213
## sex:trial 43262 4 2008659 388 2.0892 0.081543
## phase:block 2743 1 610867 97 0.4355 0.510874
## condition:phase:block 556 1 610867 97 0.0882 0.767069
## sex:phase:block 70 1 610867 97 0.0112 0.916052
## phase:trial 21661 4 1587399 388 1.3236 0.260500
## condition:phase:trial 12205 4 1587399 388 0.7458 0.561270
## sex:phase:trial 21539 4 1587399 388 1.3162 0.263277
## block:trial 258053 4 1960415 388 12.7683 8.984e-10
## condition:block:trial 31785 4 1960415 388 1.5727 0.180799
## sex:block:trial 15728 4 1960415 388 0.7782 0.539854
## phase:block:trial 41121 4 1373728 388 2.9036 0.021730
## condition:phase:block:trial 37479 4 1373728 388 2.6464 0.033203
## sex:phase:block:trial 59233 4 1373728 388 4.1825 0.002503
##
## (Intercept) ***
## condition
## sex **
## phase ***
## condition:phase
## sex:phase
## block ***
## condition:block
## sex:block
## trial ***
## condition:trial
## sex:trial .
## phase:block
## condition:phase:block
## sex:phase:block
## phase:trial
## condition:phase:trial
## sex:phase:trial
## block:trial ***
## condition:block:trial
## sex:block:trial
## phase:block:trial *
## condition:phase:block:trial *
## sex:phase:block:trial **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.51861 0.000e+00
## condition:trial 0.51861 0.000e+00
## sex:trial 0.51861 0.000e+00
## phase:trial 0.67748 2.480e-05
## condition:phase:trial 0.67748 2.480e-05
## sex:phase:trial 0.67748 2.480e-05
## block:trial 0.67189 1.791e-05
## condition:block:trial 0.67189 1.791e-05
## sex:block:trial 0.67189 1.791e-05
## phase:block:trial 0.73656 6.068e-04
## condition:phase:block:trial 0.73656 6.068e-04
## sex:phase:block:trial 0.73656 6.068e-04
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.73144 < 2.2e-16 ***
## condition:trial 0.73144 0.639643
## sex:trial 0.73144 0.103447
## phase:trial 0.84760 0.264662
## condition:phase:trial 0.84760 0.540669
## sex:phase:trial 0.84760 0.267232
## block:trial 0.84766 1.308e-08 ***
## condition:block:trial 0.84766 0.190106
## sex:block:trial 0.84766 0.520903
## phase:block:trial 0.85153 0.028885 *
## condition:phase:block:trial 0.85153 0.041956 *
## sex:phase:block:trial 0.85153 0.004366 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## HF eps Pr(>F[HF])
## trial 0.7566489 3.367593e-17
## condition:trial 0.7566489 6.455367e-01
## sex:trial 0.7566489 1.011619e-01
## phase:trial 0.8820095 2.637884e-01
## condition:phase:trial 0.8820095 5.456094e-01
## sex:phase:trial 0.8820095 2.664079e-01
## block:trial 0.8820755 7.136785e-09
## condition:block:trial 0.8820755 1.879903e-01
## sex:block:trial 0.8820755 5.254546e-01
## phase:block:trial 0.8862748 2.701715e-02
## condition:phase:block:trial 0.8862748 3.971277e-02
## sex:phase:block:trial 0.8862748 3.831438e-03## Anova Table (Type 3 tests)
##
## Response: mpm
## Effect df MSE F pes p.value
## 1 condition 1, 97 82823.09 0.95 .010 .33
## 2 sex 1, 97 82823.09 11.35 ** .10 .001
## 3 phase 1, 97 35159.81 88.24 *** .48 <.0001
## 4 condition:phase 1, 97 35159.81 1.09 .01 .30
## 5 sex:phase 1, 97 35159.81 2.23 .02 .14
## 6 block 1, 97 19549.03 52.39 *** .35 <.0001
## 7 condition:block 1, 97 19549.03 2.47 .02 .12
## 8 sex:block 1, 97 19549.03 1.47 .01 .23
## 9 trial 2.93, 283.80 7077.75 30.29 *** .24 <.0001
## 10 condition:trial 2.93, 283.80 7077.75 0.56 .006 .64
## 11 sex:trial 2.93, 283.80 7077.75 2.09 .02 .10
## 12 phase:block 1, 97 6297.60 0.44 .004 .51
## 13 condition:phase:block 1, 97 6297.60 0.09 .0009 .77
## 14 sex:phase:block 1, 97 6297.60 0.01 .0001 .92
## 15 phase:trial 3.39, 328.87 4826.86 1.32 .01 .26
## 16 condition:phase:trial 3.39, 328.87 4826.86 0.75 .008 .54
## 17 sex:phase:trial 3.39, 328.87 4826.86 1.32 .01 .27
## 18 block:trial 3.39, 328.89 5960.67 12.77 *** .12 <.0001
## 19 condition:block:trial 3.39, 328.89 5960.67 1.57 .02 .19
## 20 sex:block:trial 3.39, 328.89 5960.67 0.78 .008 .52
## 21 phase:block:trial 3.41, 330.39 4157.86 2.90 * .03 .03
## 22 condition:phase:block:trial 3.41, 330.39 4157.86 2.65 * .03 .04
## 23 sex:phase:block:trial 3.41, 330.39 4157.86 4.18 ** .04 .004
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
There was no main effect of group but a significant difference in activity between the free exploration phase and the stress phase as well as between blocks and across trials. Participants showed increased activity over time and blocks and generally lower activity in the stress phase. Complex interaction effects…
7.2 Escapes
There were no outliers with respect to escape rate.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 821.89 1 399.20 97 199.7056 < 2e-16 ***
## condition 0.54 1 399.20 97 0.1315 0.71768
## sex 10.10 1 399.20 97 2.4548 0.12042
## block 13.11 1 227.85 97 5.5809 0.02015 *
## condition:block 11.51 1 227.85 97 4.9010 0.02918 *
## sex:block 7.64 1 227.85 97 3.2506 0.07450 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Anova Table (Type 3 tests)
##
## Response: sum_escapes_block
## Effect df MSE F pes p.value
## 1 condition 1, 97 4.12 0.13 .001 .72
## 2 sex 1, 97 4.12 2.45 .02 .12
## 3 block 1, 97 2.35 5.58 * .05 .02
## 4 condition:block 1, 97 2.35 4.90 * .05 .03
## 5 sex:block 1, 97 2.35 3.25 + .03 .07
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1## contrast estimate SE df t.ratio p.value
## EC,X1 - YC,X1 -0.6021 0.371 181 -1.624 0.4382
## EC,X1 - EC,X2 -1.0254 0.276 97 -3.720 0.0020
## EC,X1 - YC,X2 -0.6378 0.371 181 -1.717 0.4382
## YC,X1 - EC,X2 -0.4233 0.371 181 -1.140 0.7679
## YC,X1 - YC,X2 -0.0358 0.353 97 -0.101 0.9196
## EC,X2 - YC,X2 0.3875 0.371 181 1.045 0.7679
##
## Results are averaged over the levels of: sex
## P value adjustment: holm method for 6 tests## Call:
## bwtrim(formula = sum_escapes_block ~ condition * factor(block),
## id = ID, data = escapesStress)
##
## value df1 df2 p.value
## condition 0.1032 1 64.2822 0.7490
## factor(block) 3.9775 1 68.5782 0.0501
## condition:factor(block) 7.0282 1 68.5782 0.0100
EC managed to escape more often in block 2 compared to block 1, whereas YC did not improve (scores denote rather a slight decrease!). Overall participants escaped more often in block 2. Men improved more than women from block 1 to block 2.
7.3 Exploration
There were some outlier with respect to exploration but since they did not affect results, we kept them.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 58881195 1 9046665 97 631.3350 < 2.2e-16
## condition 113890 1 9046665 97 1.2212 0.27187
## sex 1053931 1 9046665 97 11.3004 0.00111
## phase 3101927 1 3109569 97 96.7616 3.019e-16
## condition:phase 44758 1 3109569 97 1.3962 0.24025
## sex:phase 92948 1 3109569 97 2.8994 0.09181
## block 1122034 1 1955799 97 55.6485 3.703e-11
## condition:block 14083 1 1955799 97 0.6985 0.40536
## sex:block 85588 1 1955799 97 4.2448 0.04205
## trial 1079236 4 2230643 388 46.9308 < 2.2e-16
## condition:trial 3514 4 2230643 388 0.1528 0.96169
## sex:trial 73547 4 2230643 388 3.1982 0.01330
## phase:block 7735 1 631430 97 1.1883 0.27838
## condition:phase:block 4207 1 631430 97 0.6463 0.42342
## sex:phase:block 1481 1 631430 97 0.2276 0.63440
## phase:trial 12282 4 1504282 388 0.7920 0.53089
## condition:phase:trial 4995 4 1504282 388 0.3221 0.86317
## sex:phase:trial 21189 4 1504282 388 1.3663 0.24497
## block:trial 192152 4 2368431 388 7.8697 4.165e-06
## condition:block:trial 65567 4 2368431 388 2.6853 0.03115
## sex:block:trial 44953 4 2368431 388 1.8411 0.12019
## phase:block:trial 16311 4 1187061 388 1.3328 0.25708
## condition:phase:block:trial 33292 4 1187061 388 2.7204 0.02940
## sex:phase:block:trial 32894 4 1187061 388 2.6879 0.03102
##
## (Intercept) ***
## condition
## sex **
## phase ***
## condition:phase
## sex:phase .
## block ***
## condition:block
## sex:block *
## trial ***
## condition:trial
## sex:trial *
## phase:block
## condition:phase:block
## sex:phase:block
## phase:trial
## condition:phase:trial
## sex:phase:trial
## block:trial ***
## condition:block:trial *
## sex:block:trial
## phase:block:trial
## condition:phase:block:trial *
## sex:phase:block:trial *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Mauchly Tests for Sphericity
##
## Test statistic p-value
## trial 0.48740 0.000000
## condition:trial 0.48740 0.000000
## sex:trial 0.48740 0.000000
## phase:trial 0.74625 0.000983
## condition:phase:trial 0.74625 0.000983
## sex:phase:trial 0.74625 0.000983
## block:trial 0.58692 0.000000
## condition:block:trial 0.58692 0.000000
## sex:block:trial 0.58692 0.000000
## phase:block:trial 0.85865 0.104399
## condition:phase:block:trial 0.85865 0.104399
## sex:phase:block:trial 0.85865 0.104399
##
##
## Greenhouse-Geisser and Huynh-Feldt Corrections
## for Departure from Sphericity
##
## GG eps Pr(>F[GG])
## trial 0.71174 < 2.2e-16 ***
## condition:trial 0.71174 0.92027
## sex:trial 0.71174 0.02605 *
## phase:trial 0.88043 0.51682
## condition:phase:trial 0.88043 0.84018
## sex:phase:trial 0.88043 0.24917
## block:trial 0.79186 3.059e-05 ***
## condition:block:trial 0.79186 0.04373 *
## sex:block:trial 0.79186 0.13632
## phase:block:trial 0.92943 0.25920
## condition:phase:block:trial 0.92943 0.03308 *
## sex:phase:block:trial 0.92943 0.03479 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## HF eps Pr(>F[HF])
## trial 0.7355075 2.443288e-24
## condition:trial 0.7355075 9.250713e-01
## sex:trial 0.7355075 2.462910e-02
## phase:trial 0.9176656 5.213944e-01
## condition:phase:trial 0.9176656 8.478121e-01
## sex:phase:trial 0.9176656 2.478935e-01
## block:trial 0.8217060 2.296138e-05
## condition:block:trial 0.8217060 4.164536e-02
## sex:block:trial 0.8217060 1.338942e-01
## phase:block:trial 0.9710776 2.579624e-01
## condition:phase:block:trial 0.9710776 3.085603e-02
## sex:phase:block:trial 0.9710776 3.250938e-02## Anova Table (Type 3 tests)
##
## Response: exploration
## Effect df MSE F pes p.value
## 1 condition 1, 97 93264.59 1.22 .01 .27
## 2 sex 1, 97 93264.59 11.30 ** .10 .001
## 3 phase 1, 97 32057.41 96.76 *** .50 <.0001
## 4 condition:phase 1, 97 32057.41 1.40 .01 .24
## 5 sex:phase 1, 97 32057.41 2.90 + .03 .09
## 6 block 1, 97 20162.88 55.65 *** .36 <.0001
## 7 condition:block 1, 97 20162.88 0.70 .007 .41
## 8 sex:block 1, 97 20162.88 4.24 * .04 .04
## 9 trial 2.85, 276.15 8077.53 46.93 *** .33 <.0001
## 10 condition:trial 2.85, 276.15 8077.53 0.15 .002 .92
## 11 sex:trial 2.85, 276.15 8077.53 3.20 * .03 .03
## 12 phase:block 1, 97 6509.58 1.19 .01 .28
## 13 condition:phase:block 1, 97 6509.58 0.65 .007 .42
## 14 sex:phase:block 1, 97 6509.58 0.23 .002 .63
## 15 phase:trial 3.52, 341.61 4403.56 0.79 .008 .52
## 16 condition:phase:trial 3.52, 341.61 4403.56 0.32 .003 .84
## 17 sex:phase:trial 3.52, 341.61 4403.56 1.37 .01 .25
## 18 block:trial 3.17, 307.24 7708.64 7.87 *** .08 <.0001
## 19 condition:block:trial 3.17, 307.24 7708.64 2.69 * .03 .04
## 20 sex:block:trial 3.17, 307.24 7708.64 1.84 .02 .14
## 21 phase:block:trial 3.72, 360.62 3291.73 1.33 .01 .26
## 22 condition:phase:block:trial 3.72, 360.62 3291.73 2.72 * .03 .03
## 23 sex:phase:block:trial 3.72, 360.62 3291.73 2.69 * .03 .03
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
There was no main effect of group but a significant difference in exploration between the free exploration phase and the stress phase as well as between blocks and across trials. Participants showed increased exploration over time and blocks and generally lower exploration in the stress phase. The interaction of condition x phase x trial indicated that YC explored much more during the stress phase than EC and this difference became more pronounced over trials.
7.4 Efficiency
There were some outliers with respect to efficiency but excluding them did not affect the results, so we kept them.
##
## Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
##
## Sum Sq num Df Error SS den Df F value Pr(>F)
## (Intercept) 1567728 1 408847 92 352.7745 < 2.2e-16 ***
## condition 7523 1 408847 92 1.6928 0.196479
## sex 1769 1 408847 92 0.3980 0.529686
## block 9880 1 311431 92 2.9188 0.090925 .
## condition:block 36074 1 311431 92 10.6567 0.001541 **
## sex:block 14371 1 311431 92 4.2453 0.042183 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Anova Table (Type 3 tests)
##
## Response: overall_efficiency
## Effect df MSE F pes p.value
## 1 condition 1, 92 4443.99 1.69 .02 .20
## 2 sex 1, 92 4443.99 0.40 .004 .53
## 3 block 1, 92 3385.11 2.92 + .03 .09
## 4 condition:block 1, 92 3385.11 10.66 ** .10 .002
## 5 sex:block 1, 92 3385.11 4.25 * .04 .04
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1## contrast estimate SE df t.ratio p.value
## EC,X1 - YC,X1 15.39 13.2 181 1.166 0.6441
## EC,X1 - EC,X2 13.50 10.8 92 1.249 0.6441
## EC,X1 - YC,X2 -27.75 13.2 181 -2.104 0.1472
## YC,X1 - EC,X2 -1.89 13.2 181 -0.143 0.8863
## YC,X1 - YC,X2 -43.14 13.6 92 -3.178 0.0121
## EC,X2 - YC,X2 -41.25 13.2 181 -3.127 0.0121
##
## Results are averaged over the levels of: sex
## P value adjustment: holm method for 6 tests## Call:
## bwtrim(formula = overall_efficiency ~ condition * factor(block),
## id = ID, data = efficiencyStress)
##
## value df1 df2 p.value
## factor(block) 1.9489 1 40.8194 0.1703
## condition 0.6105 1 33.9118 0.4400
## factor(block):condition 4.8779 1 33.9118 0.0341Whereas EC and YC did not differ in efficiency in block 1 (although YC had slightly better scores), YC showed sig. less efficient behaviour in block 2 compared to EC. There was also an interaction of sex x block.
8 Plots for Paper
8.1 Figure 1
8.2 Figure 2
